The overall thrust of the research objectives is to make progress towards providing, for a wide variety of applications and experimental designs, a semi-parametric alternative to the popular parametric regression methods used in the analysis of data. Methodology is proposed for discrete and continuous data as well as for independent and correlated responses. The objectives are to study; i) nonparametric estimation of a regression function when the explanatory variable is discrete, ii) estimation of the dose effect given observations over time in a dose-response experiment, and nonparametric detection of interactions between dose and time, iii) estimation in conditionally specified distributions. Decisions and recommendations based on data analysis using the wrong parametric model are not reliable. Therein lies the need for the development of methodology for fitting semiparametric models to data. The basic research efforts outlined in this proposal include: I) theoretical work, ii) computer simulations to validate the procedures, and iii) application of the semiparametric methods to biomedical data obtained from researchers at Virginia Commonwealth University - Medical College of Virginia, The University of Texas M.D. Anderson Cancer Center, and The Eye Institute of the University of Wisconsin, Madison. This project also includes an undergraduate student mentorship and community outreach component. Undergraduate students in the Department of Mathematical Sciences will assist with the research projects and with mathematics outreach activities designed for the El Paso area Middle School students.